274 research outputs found
Undulation instabilities in the meniscus of smectic membranes
Using optical microscopy, phase shifting interferometry and atomic force
microscopy, we demonstrate the existence of undulated structures in the
meniscus of ferroelectric smectic-C* films. The meniscus is characterized by a
periodic undulation of the smectic-air interface, which manifests itself in a
striped pattern. The instability disappears in the untilted smectic-A phase.
The modulation amplitude and wavelength both depend on meniscus thickness. We
study the temperature evolution of the structure and propose a simple model
that accounts for the observed undulations.Comment: Submitted to PR
Electrooptic soft mode response of compounds exhibiting the antiferroelectric phase
We report measurements on the electrooptic response of thin samples (~2-5 μm) of two antiferroelectric liquid crystals. All the phase transitions in these compounds can be very easily detected using this technique. We have been able to measure such an electrooptic effect for the first time in the antiferroelectric and smectic I∗ phases of a tolane compound. The response shows a relaxation at high frequencies (~10 KHz) and is at-tributed to a soft mode which produces an asymmetry in the molecular tilt in successive layers
A constructive study of the module structure of rings of partial differential operators
The purpose of this paper is to develop constructive versions of Stafford's theorems on the module structure of Weyl algebras A n (k) (i.e., the rings of partial differential operators with polynomial coefficients) over a base field k of characteristic zero. More generally, based on results of Stafford and Coutinho-Holland, we develop constructive versions of Stafford's theorems for very simple domains D. The algorithmization is based on the fact that certain inhomogeneous quadratic equations admit solutions in a very simple domain. We show how to explicitly compute a unimodular element of a finitely generated left D-module of rank at least two. This result is used to constructively decompose any finitely generated left D-module into a direct sum of a free left D-module and a left D-module of rank at most one. If the latter is torsion-free, then we explicitly show that it is isomorphic to a left ideal of D which can be generated by two elements. Then, we give an algorithm which reduces the number of generators of a finitely presented left D-module with module of relations of rank at least two. In particular, any finitely generated torsion left D-module can be generated by two elements and is the homomorphic image of a projective ideal whose construction is explicitly given. Moreover, a non-torsion but non-free left D-module of rank r can be generated by r+1 elements but no fewer. These results are implemented in the Stafford package for D=A n (k) and their system-theoretical interpretations are given within a D-module approach. Finally, we prove that the above results also hold for the ring of ordinary differential operators with either formal power series or locally convergent power series coefficients and, using a result of Caro-Levcovitz, also for the ring of partial differential operators with coefficients in the field of fractions of the ring of formal power series or of the ring of locally convergent power series. © 2014 Springer Science+Business Media
Dislocation loops in overheated free-standing smectic films
Static and dynamic phenomena in overheated free-standing smectic-A films are
studied using a generalization of de Gennes' theory for a confined presmectic
liquid. A static application is to determine the profile of the film meniscus
and the meniscus contact angle, the results being compared with those of a
recent study employing de Gennes' original theory. The dynamical generalization
of the theory is based on on a time-dependent Ginzburg-Landau approach. This is
used to compare two modes for layer-thinning transitions in overheated films,
namely "uniform thinning" vs. nucleation of dislocation loops. Properties such
as the line tension and velocity of a moving dislocation line are evaluated
self-consistently by the theory.Comment: 16 pages, 8 figure
Modeling Dipolar and Quadrupolar Defect Structures generated by Chiral Islands in Freely-Suspended Liquid Crystal Films
We report a detailed theoretical analysis of novel quadrupolar interactions
observed between islands, which are disk-like inclusions of extra layers,
floating in thin, freely suspended smectic C liquid crystal films. Strong
tangential anchoring at the island boundaries result in a strength +1 chiral
defect in each island and a companion -1 defect in the film, these forming a
topological dipole. While islands of the same handedness form linear chains
with the topological dipoles pointing in the same direction, as reported in the
literature, islands with different handedness form compact quadrupolar
structures with the associated dipoles pointing in opposite directions. The
interaction between such heterochiral island--defect pairs is complex, with the
defects moving to minimize the director field distortion as the distance
between the islands changes. The details of the inter-island potential and the
trajectories of the -1 defects depend strongly on the elastic anisotropy of the
liquid crystal, which can be modified in the experiments by varying the
material chirality of the liquid crystal. A Landau model that describes the
energetics of freely mobile defects is solved numerically to find equilibrium
configurations for a wide range of parameters.Comment: 8 pages, 9 figure
TP53 and MDM2 single nucleotide polymorphisms influence survival in non-del(5q) myelodysplastic syndromes
Abstract:P53 is a key regulator of many cellular processes and is negatively regulated by the human homolog of murine double minute-2 (MDM2) E3 ubiquitin ligase. Single nucleotide polymorphisms (SNPs) of either gene alone, and in combination, are linked to cancer susceptibility, disease progression, and therapy response. We analyzed the interaction of TP53 R72P and MDM2 SNP309 SNPs in relationship to outcome in patients with myelodysplastic syndromes (MDS). Sanger sequencing was performed on DNA isolated from 208 MDS cases. Utilizing a novel functional SNP scoring system ranging from +2 to -2 based on predicted p53 activity, we found statistically significant differences in overall survival (OS) (p = 0.02) and progression-free survival (PFS) (p = 0.02) in non-del(5q) MDS patients with low functional scores. In univariate analysis, only IPSS and the functional SNP score predicted OS and PFS in non-del(5q) patients. In multivariate analysis, the functional SNP score was independent of IPSS for OS and PFS. These data underscore the importance of TP53 R72P and MDM2 SNP309 SNPs in MDS, and provide a novel scoring system independent of IPSS that is predictive for disease outcome
Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals
Lattice statistical mechanics, often provides a natural (holonomic) framework
to perform singularity analysis with several complex variables that would, in a
general mathematical framework, be too complex, or could not be defined.
Considering several Picard-Fuchs systems of two-variables "above" Calabi-Yau
ODEs, associated with double hypergeometric series, we show that holonomic
functions are actually a good framework for actually finding the singular
manifolds. We, then, analyse the singular algebraic varieties of the n-fold
integrals , corresponding to the decomposition of the magnetic
susceptibility of the anisotropic square Ising model. We revisit a set of
Nickelian singularities that turns out to be a two-parameter family of elliptic
curves. We then find a first set of non-Nickelian singularities for and , that also turns out to be rational or ellipic
curves. We underline the fact that these singular curves depend on the
anisotropy of the Ising model. We address, from a birational viewpoint, the
emergence of families of elliptic curves, and of Calabi-Yau manifolds on such
problems. We discuss the accumulation of these singular curves for the
non-holonomic anisotropic full susceptibility.Comment: 36 page
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